diagnosing a blown fuse

I've followed all the advice I've received here and from other sources - what do I do next? (other than the obvious - call an electrician!)

I have one 20 amp screw-in fuse that blows.

So far, I have done the following:

Physically disconnected all the solid copper wires that I can identify as being on the circuit. A digital multimeter still shows between 0 and 3 ohms between the live and common (black and white) wires, unless the device is out of the circuit by up-circuit disconnections. (50 year old house - no ground.)

Removed the live wire from the fuse block - I was told that it the fuse still blows, I have a bad fuse block - it doesn't.

Compared voltage and resistance between this circuit and a known good circuit in the fuse box - similar.

Sorry to hear that you have not found your short. You should not get any continuity between the white and black wires if all devices are disconnected. If you still have a short it must be in the wire between the electrical devices. Maybe the wire got too hot and melted together or a nail or screw penetrated the wire if you have been hanging pictures or doing some kind of home repair, or the wire was run through some kind of pinch point in the attic and the house settled pinching the wire. What you will need to do is determine where the short is and wire around it. To do this find the "in" wires in each electric box on the circuit, and the "out" wires and seperate them. Check for continuity between the wires in each direction from that point. When you find the first time you show 0 ohms you have found the direction of your short from that point, and that will be the wires that need to be replaced. Good luck.